People always talk about corruption in politics as if the problem we need to solve reduces to some form of quid pro quo. Ian Ayres and Bruce Ackerman, for example, suggest an scheme to anonymize transactions to the point that quids can't be guaranteed, and suggest this will eliminate or greatly reduce quos.
Unfortunately, corruption of the political system (grand corruption, if you will) does not depend on individual corruption (petty corruption). There are no doubt dishonest politicians looking for handouts in return for favors, but there are plenty of true believers out there who would pursue the same policy goals honestly and sincerely, and as long as money speaks, the true believers who align with the interests of money will get the support of money. True believers may actually be worse representatives than corrupt opportunists. An opportunist, after all, will do anyone a favor for a price. True believers only represent those whose views match their own.